Pilot symbol assisted modulation (PSAM) is a known method used to reduce effects of fading and other distortion factors in mobile communications, by periodically inserting known pilot symbols in the signal data stream. Since the transmitted pilot symbols are known, the receiver can make use of these regularly spaced pilot symbols to derive the amplitude and phase reference of the received signal. Channel estimators are used to determine the amplitude and phase reference at the known pilot symbols, providing correction factors that can then be interpolated and applied to the other symbols (data symbols) in the signal. There is, in general, a tradeoff between the complexity of the acquisition algorithm and its robustness. Two types of algorithms used for frequency acquisition are differential decoding and coherent correlation (see below).
The robustness of frequency estimation for a data packet in noise depends on the pattern of pilot symbols throughout the packet. The most robust methods use the Fourier Transform. In this method, the data symbols are identified and removed, leaving the pilot symbols. A Fourier Transform (typically, the Fast Fourier Transform—FFT) is then applied to the resulting packet in order to identify the maximum-likelihood frequency.
Pilot symbols do not carry any data, and it is therefore necessary to keep them to as few as possible. However, too few pilot symbols can result in performance degradation due to poor channel estimation. The trade-off between pilot symbol spacing and the symbol error rate is therefore an important consideration for system of this type.
The dominant method of TDMA packet acquisition uses contiguous blocks of pilot symbols, known as Unique Words (UW) often coded with binary phase shift keying (BPSK) to allow identification of the packet's time offset. Fast algorithms have been developed for UW packet acquisition.
If a single UW is used alone, the frequency acquisition is poor. Methods have therefore been developed to spread pilot symbols over the length of the packet. Two methods are commonly used to improve frequency offset estimation in such packet acquisition:    1. Pilot symbols regularly spaced throughout the packet. Once the contiguous block of UWs has been used to establish the packet's timing, the channel can be sampled at regular intervals and the pilot symbols throughout the packet may be used to identify the frequency to an acceptable resolution. This divides the UW into two parts, each used for different tasks, which is not computationally efficient. Ideally, all pilot symbols should be used for both time and frequency acquisition.    2. Two UWs, one placed at either end of the packet. The phase between the leading and trailing pilot symbol UWs gives a precise frequency estimate. However, such methods can tend to distinguish poorly between certain frequency alternatives, as no pilot symbol data is available throughout the bulk of the packet.
Coherent correlation methods are comparatively fast. In such techniques, the majority of the pilot symbols are in a UW at the front of the packet. A frequency offset is applied to the UW symbols before they are summed. However, if the frequency offset is not close to the signal's actual frequency, symbols in the UW can cancel one another, and the SNR will thus be significantly decreased. To overcome this, coherent correlation must be repeated at a number of different frequency offsets, such that at least one frequency option is sufficiently close to the actual frequency. This repetition increases the complexity, and the technique is less robust than the Fourier Transform frequency response method described above.
Differential decoding methods are also comparatively fast, and they need not deal with coherence issues. However, they decrease the effective SNR by multiplying noise data symbols together. To overcome this, differential decoding must be repeated at several different time-offsets, which once again increases the algorithm complexity. The technique cannot improve on a performance dictated by the pattern of pilot symbols.
Methods have been proposed in the past for pilot structures relying on non-uniform spacing, such as that postulated in ‘A study of Non-Uniform Pilot Spacing for PSAM’, Lo, H., Lee, D. and Gansman, J. A., IEEE 2000, Proc ICC International Conference on Communications, Volume 1, 18-22 Jun. 2000, pp. 322-325. This paper examines a number of alternative structures, and concludes that performance can theoretically be improved without increasing the number of pilot symbols by using non-uniform distributions, especially at high Doppler rates and in the presence of an unknown frequency offset. However, the paper does not consider optimisation, and the non-uniform structures considered are in fact repeating regular patterns.
There is scope to improve the robustness of frequency acquisition by improved selection of the pattern of pilot symbols.